High-accuracy FDTD solution of the absorbing wave equation, and conducting Maxwell's equations based on a nonstandard finite-difference model
High-accuracy FDTD solution of the absorbing wave equation, and conducting Maxwell's equations based on a nonstandard finite-difference model
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DOI：
10.1109/tap.2004.823874
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发表时间：
2004-04
影响因子：
5.7
通讯作者：
J. B. Cole
中科院分区：
文献类型：
--
作者：
J. B. Cole
在此之前，我们介绍了基于非标准有限差分（NSFD）的高精度时域有限差分（FDTD）算法来求解非吸收波动方程和非导电麦克斯韦方程。现在我们把我们的方法推广到吸收波方程和传导麦克斯韦方程。我们首先推导了一维波动方程的精确NSFD模型，并将其推广到求解二维和三维的吸收波方程和传导麦克斯韦方程组的高精度FDTD算法。对于网格间距h和波长/spl lambda/，NSFD解的误差为/spl epsiv//spl sim/（h//spl lambda/）/sup 6/，而对于使用二阶中心有限差分的普通FDTD算法为（h//spl lambda/）/sup 2/。这种高精度不是通过使用高阶有限差分实现的，而是通过利用衰减谐波解基函数的分析性质实现的。除了更高的精度，在NSFD算法中的最大时间步长可以比普通的二阶FDTD算法稍长。
We previously introduced high-accuracy finite-difference time-domain (FDTD) algorithms based on nonstandard finite differences (NSFD) to solve the nonabsorbing wave equation and the nonconducting Maxwell equations. We now extend our methodology to the absorbing wave equation and the conducting Maxwell equations. We first derive an exact NSFD model of the one-dimensional wave equation, and extend it to construct high-accuracy FDTD algorithms to solve the absorbing wave equation, and the conducting Maxwell's Equations in two and three dimensions. For grid spacing h, and wavelength /spl lambda/, the NSFD solution error is /spl epsiv//spl sim/(h//spl lambda/)/sup 6/ compared with (h//spl lambda/)/sup 2/ for ordinary FDTD algorithms using second-order central finite-differences. This high accuracy is achieved not by using higher-order finite differences but by exploiting the analytical properties of the decaying-harmonic solution basis functions. Besides higher accuracy, in the NSFD algorithms the maximum time step can be somewhat longer than for the ordinary second-order FDTD algorithms.